Question

If tantheeta =
1/✓5
and theeta lies in third quadrant then value of sintheeta is :​

Answer 1

Explanation:

Correct option is

C

5

−1

Ans. (c)

Since θ lies in the third quadrant,

cosθ<0 or sinθ=−4/5⇒cosθ=−3/5

Now , cos

2

(θ/2)=

2

1

(1+cosθ)

=

2

1

(1−

5

3

)=

5

1

since 180

o

<θ<270

o

, we have 90

o

<

2

θ

<135

o

so that

2

θ

lies in the second quadrant.

Hence cos(

2

θ

) is negative. Therefore (1) gives $ cos(

2

θ

) =-1\sqrt { 5 }$$.